Evaluation of viscous drag reduction schemes for subsonic transports

NASA CR-132718 ATL TR 216 EVALUATION OF VISCOUS DRAG REDUCTION SCHEMES FOR SUBSONIC TRANSPORTS By A. Marino, C. Economos and F. G. Howard (NASA-CF-132718) EVAlUATION nv VISCOUS DRAG N16-13013 REDUCTION SCHEMES FCR SUBSCNIC TRANSPCRTS (Advanced Technolo9j labs.) 114 p He $5.50 CSCL 01C Unclas G3/02 01896 ADVANCED TECHNOLOGY LABORATORIES, INC.

Prepared for NATIONAL AERONAUTICS AND SPACE ADMINISTRATION NASA Langley Research Center Contract NASl-13286

TABLE OF CONTENTS Page INTRODUCTION I.

LI STOF SYMBOLS II.

PREliMINARY CONSIDERATIONS I" .

A. BASELINE AIRCRAFT DRAG B. FUSELAGE GEOMETRY AND PRESSURE DISTRIBUTION C.. WING GEOMETRY AND PRESSURE DISTRIBUTION ~ BOUNDARY LAYER CALCULATIONS IV.

A. CONSTANT PRESSURE LAMINAR RESULTS B. LAMINAR RESULTS WITH PRESSURE GRADIENT C. TURBULENT RESULTS WITH SLOT INJECTION V. DRAG REDUCTION RESULTS A. FUSELAGE SLOT INJECTION B. COMBINED FUSELAGE SUCTION AND SLOT INJECTION C. FUSELAGE SUCTION D. WING SUCTION MISSION PERFORMANCE VI.

CONCLUDING REMARKS VII.

REFERENCES APPENDIX A - LAMINAR BOUNDARY LAYER HITH SIMUL- TANEOUS MASS TRANSFER AND PRESSURE GRADIENT APPENDIX B - LIFT AUGMENTATION 'DUE TO WING SUCTION -i i i-

LI ST OF FIGURES Page ~ r 8 , ~ FUSELAGE GEOMETRY AND PRESSURE DISTRIBUTION FIG, 1.

PRESSURE DISTRIBUTION ON WING FIG. 2.

WING GEOMETRY FIG.

3.

DRAG COEFFICIENT FOR FLAT PLATE WITH UNIFORM FIG. It.

SUCT;ON lIt R~DUCED SKIN FRICTION COEFFICIENT WITH SUCTION FIG. 5.

CHORDWISE VARIATION OF SUCTION PARAMETER ON FIG. 6.

WING SURFACES CHORDWISE VARIATION OF LOCAL SKIN FRICTION FIG.

7.

ON WING SURFACES INITIAL VELOCITY PROFILE AT FIRST SLOT AND FIG. 8.

PRESSURE VARIATION TO FIRST SLOT VELOCITY DEVELOPMENT AND SKIN FRICTION FIG. 9.

BEHAVIOR DOWNSTREAM OF A SINGLE SLOT SKIN FRICTION REDUCTION WITH SLOT INJECTION, FIG. 10.

h = 7.62 em, (V/V) = 0.338 max FIG. 11. VARIATION OF LOCAL SKIN FRICTION ON FUSELAGE WITH SLOT INJECTION: M. = 0.2 23 J FIG. 12. SKIN FRICTION REDUCTION EFFECTIVENESS AS A 2It FUNCTION OF NUMBER OF SLOTS FIG. 13. SKIN FRICTION REDUCTION EFFECTIVENESS AS A FUNCTIO~ OF SLOT HEIGHT AND INJECTION MACH NUMBER VELOCITY PROFILES AT END OF FUSELAGE: 10 FIG. lIt • SLOTS WITH M. = 0.2 J SCHEMATIC OF SLOT INJECTION SYSTEM 30 FIG.

15.

BOUNDARY LAYER AT END OF AVERAGE VELOCITY IN FIG. 16a.

SLOTS; M. = 0.2 J OF AVERAGE VELOCITY IN BOUNDARY LAYER AT END FIG. 16b.

SLOTS; M. = O. 1 J -iv-

FIGURES (Continued) LIST OF Page HANDLING WITH COMPRESSOR VELOCITIES AVERAGE 17a.

FIG.

M. = 0.2 LAYER; OF BOUNDARY INNER FLOW J HANDLING WITH COMPRESSOR VELOCITIES AVERAGE 17b.

FIG.

0.1 M. = INNER FLOW; J HANDLING TURBINE WITH VELOCITIES 18a. AVERAGE FIG.

M. = 0.2 LAYER; OF BOUNDARY INNER FLOW J HANDLING WITH TURBINE VELOCITIES AVERAGE 18b.

FIG.

= 0.1 FLOW; M.

INNER J COMPRESSOR SLOT INJECTION, DRAG WITH NET FIG. 19a.

M. = 0.2 = 15.24 em, FLOW; h INNER HANDLING J HANDLING TURBINE INJECTION, WITH SLOT NET DRAG 19b.

FIG.

0.2

em, M. =

h = 15.24

FLOW; INNER J COMPRESSOR INJECTION, WITH SLOT NET DRAG 20a.

FIG.

= 0.2

7.62 em, M.

FLOW; h =

INNER HANDLING J HANDLING TURBINE INJECTION, WITH SLOT NET DRAG FIG. 20b.

M. = 0.2

7.62 em,

FLOW; h =

INNER J COMPRESSOR SLOT INJECTION, DRAG WITH 21a. NET FIG.

M. = 0.2 = 3.81 em, FLOW; h INNER HANDLING J , HANDLING TURBINE INJECTION, WITH SLOT NET DRAG 21b.

FIG.

M. = 0.2 = 3.81 em, FLOW; h INNER J f ,~ WITH TURBINE/COMPRESSOR OF NET DRAG 22. COMPARISON FIG.

FLOW; LAYER FLOW AND BOUNDARY STREAM USING FREE

= 0.2

M.

J INNER FLOW; HANDLING WITH COMPRESSOR NET DRAG FIG. 23.

j = 0.1 M FLOW; INNER TURBINE HANDLING DRAG WITH 24. NET FIG.

0.1 M. = J DRAG; ON NET MACH NUMBER INJECTION EFFECT OF FIG. 25.

= 3.81 em h AS A REDUCTION DRAG DESCRIBING PARAMETER FIG. 26.

HEIGHT OF SLOT FUNCTION AND SUCTION COMBINED DRAG WITH REDUCED FIG. 27.

INJECTION -v-

LI ST OF FIGURES (Continued) Page FIG. 28. SCHEMATIC JF FUSELAGE SUCTION SYSTEM WITH TURBO-MACHINES 61 AVERAGE VELOCITY IN SUCTION BOUNDARY LAYER 62 FIG. 29.

FIG. EFFECT OF COMPRESSOR DISCHARGE MACH NUMBER 30.

ON PRESSURE RATIOS AND NET DRAG WITH FUSE- LAGE SUCTION FIG. NET DRAG WITH FUSELAGE SUCTION 66 31..

FIG. 32. EFFECT OF TURBO-MACHINE EFFICIENCIES AND LINE LOSS RECOVERY FACTOR ON NET DRAG WITH FUSELAGE SUCTION FIG.

33. SCHEMATIC OF WING SUCTION ARRANGEMENT FIG. 34. EFFECT OF EXIT MACH NUMBERS ON NET DRAG WITH WING SUCTION FIG. EFFECT OF TURBINE ENTRANCE AND EXIT MACH 35.

NUMBERS ON NET DRAG WITH WING SUCTION FIG.

36. EFFECT OF AVERAGE SUCTION PRESSURE ON NET DRAG WITH WING SUCTION FIG. EFFECT OF TURBO-MACHINE EFFICIENCIES AND 37.

LINE LOSS RECOVERY FACTORS ON NET DRAG WITH WING SUCTION FIG. 38. INCREASED MAXIMUM LID WITH NET REDUCED DRAG i FIG. INCREASED RANGE WITH FUSELAGE DRAG REDUCTION I 39.

.J AS FUNCTION OF SURFACE WEIGHT PARAMETER FIG. DECREASED FUEL LOAD WITH FUSELAGE DRAG RE- 40.

DUCTION AS FUNCTION OF SURFACE WEIGHT PARAMETER ..

FIG. 41. EFFECT OF TURBO-MACHINE EFFICIENCIES AND LINE , LOSS RECOVERY FACTOR ON INCREASED RANGE WITH I FUSELAGE SUCTION i FIG. 42. EFFECT OF TURBO-MACHINE EFFICIENCIES AND LINE ~ J LOSS RECOVERY FACTOR ON REDUCED FUEL LOAD WITH FUSELAGE SUCTION 86 1 \ FIG. 43. INCREASED RANGE WITH DRAG REDUCTION SCHEMES AS

J

FUNCTION OF SURFACE WEIGHT pARAMETER -vi -

LIST OF FIGURES (Continued) Page FIG. 44. DECREASED FUEL LOAD WITH DRAG REDUCTION SCHEMES AS FUNCTION OF SURFACE WEIGHT PARAMETER 88 FIG. 45. EFFECT OF TURBO-MACHINE EFFIC1ENCIES AND LINE LOSS RECOVERY FACTOR ON INCREASED RANGE WITH COMBINED FUSELAGE AND WING DRAG REDUCTION SCHEME 91 FIG. 46. EFFECT OF TURBO-MACHINE EFFICIENCIES AND LINE LOSS RECOVERY FACTOR ON DECREASED FUEL LOAD WITH COMBINED FUSELAGE AND WING DRAG REDUCTION SCHEME 92 APPENDIX A FIG. A-1. CHORDWISE VARIATION OF LOCAL SKIN FRICTION AND SEPARATION ON AN AIRFOIL WITH UNIFORM SUCTION 101 FIG. A-2. NET REDUCTION IN AVERAGE SKIN FRICTION DRAG AS A FUNCTION OF SUCTION PARAMETER 102 -vi i-

SUMMARY drag of viscous study a theoretical results of the describes This report sub- of a 'long-haul fuselage to the application potential for schemes reduction tangential included The schemes which were examined aircraft.

transport sonic tangen- of combinations synergetic and various fuselage on the injection slot sur- and fuselage to wing applied suction distributed and slot injection tial systems turbo-machinery) utilizing (i.e., and mechanical passive faces. Both examined.

were a fixed sub- at was determined systems selected of the performance Overall and an

M = 0.8

number of Mach to a flight corresponding cruise condition sonic performance of the to which most aircraft nominal m. The of 11,000 altitude Some 747 category.

~oeing of the transport ~ wide-body was was referenced data to a Lock- referenced are wing suction with results obtained the performance of section.

wing Star Lifter heed c-141 fuselage in reductions substantial that very study show of this The results drag the However, slot injection.

with tangential achievable drag are viscous the turbo- viz., baseline design, of the components to the attributable penalties drag. In viscous in fuselage the reduction offset ducts, largely and machinery penalties The drag system.

to the drag accrues in a net increase cases, some air used captured of the the momentum

reducing {

process of in the Incurred are ff ...

in the Perturbations ducts.

through the this air pumping and in 'njection for at equally slots distributed of ten (10) use which involved design, baseline that any indicate did n~t the fuselage, length of over the spaced intervals was possible the baseJinedeslgn of the performance in improvement significant alternate that if it isc1ear However, variations.

minor parametric through and pumping capturing with associated system penalties the which avoid designs pro- per se, can slot injection, be devised, air can rates of weight .flow high minimal 50%) with large as (i.e., as drag reductions viscous significant duce configuration.

basic fuselage on the and impact complexity combinations study involved the present in investigated designs ,Alternate fuselage, on the and injection surfaces the wing suction on layer of boundary only.

to the fuselage applied combinations and injection and suction -viii-

Overall system performance for these designs is found to be superior to the baseline injection scheme, due primarily to reduction of the requisite flow rates. The latter are based on theoretical estimates of the suction re- quired to maintain a laminar condition in two-dimensional incompressible bound- ary layer flow. Whether these theoretical estimates will prove valid under ac- tual fl ight con.ditions is not known. Nevertheless"with'this caveat in mind, it is shown that the considered alternate designs offer significant improvements in fuel consumption and/or range characteristics. Fuel load decreases of the order of 5 to 17% an'd range increases of 8 to 32% are obta i ned •

I. INTRODUCTION The objective of the present study was to evaluate quantitatively a fuse- lage viscous drag reduction system for a representative subsonic aircraft. At its inception, this study was structured around a baseline scheme which in- volved tangential slot injection through ten (10) slots at equally spaced in- tervals along the fuselage. The study was to include theoretical calculations for all system components, including rotating machinery performance and effi- ciency and duct losses.

In the course of this investigation it was found that the baseline scheme was incapable of providing the anticipated overall s~stem drag reduction and, in some cases, resulted in increased overall system drag. Accordingly, with the agreement of NASA, alternate schemes were examined. These involved the use of boundary layer suction on both fuselage and wing surfaces in various combinations with slot injection. These schemes have been found to provide sighificant improvement in overall performance.

The efficacy of boundary layer suction in reducing viscous drag resides in the generally recognized principle that suction can stabilize a laminar boundary layer. As a result, the skin friction on a surface through which suction is applied can be reduced to a small fraction of its value for the naturally turbulent boundary layer on the same surface.

Experimental evidence exists demonstrating the abilitY'of suction to main- t~ining a laminar flm</ for the conditions of interest in the present investi- gation under ideal conditions. For the subsonic case the results Df Refer~ ences (1) and (2) may be cited. The results pf Pfenninger (Reference 3) indi-' cate that simi lar results can be achieved for supersonic flow for a length Reynolds number up to 5 x 10 , The feasibility of suppressing separation and maintaining laminar flow in and downstream of interactions with \</eak incident shock waves has been demonstratet:l by the experiments of Groth et al(Reference 4)1~ On the other hand, experience shows that there are formidable problems associated with utilizing laminar flm</ control when nonuniformities in the suc- tion distribution and/or surface geometry are present. As will be seen later, the schemes which are examined here inherently involve such nonuniformities .

In addition, the fabrication, operation and maintenance problems associated with a suitable porous surface have not been addressed in this study. Ac- cordingly, while the results presented here delineate the potential of these schemes, they should be considered provisional in terms of application.

In the present study the potential benefit in performance due to suction techniques was examined in two distinct ways. In the first of these, suction was applied to essentially constant pressure surfaces (fuselage) to stabilize a laminar boundary layer so as to prevent transition and the associated in- creases in viscous shear stress on the sl~rface. In the second approach, suc-" tion was applied to wing surfaces experiencing adverse pressure gradients with the aim of preventing separation. In these circumstances, improvement in'aircraft aerodynamic performance would accrue both from reduction in vis- cous shear as well as from improved LID characteristics of the wing.

Theoretical estimates of viscous drag reduction due to tangential slot injection were provided by the NASA Langley Research Center in accordance with contractual agreement. Corresponding estimates of laminar boundary layer behavior with suction were generated by ATL employing various approxi.- mate schemes which are described in subsequent sections of this report.

The overall performance of the selected systems was determined at a fixed subsonic cruise condition corresponding to a nominal flight Mach number of

M = 0.8 and an altitude of 11,000 m. The aircraft configuration to which

most of the performance data was r.eferenced was the Boeing 747. Some of the performance results obtained with wing suction are referenced to a Lockheed C-141 Star Lifter wing section. In this connection it must be emphasized that no optimization in terms of aircraft configuration was attempted in the present study. Accordingly, the results obtained can probably be improved by appropriate changes in configuration. Recommendations in this regard are presen~ed in the last section of this report.

II. liST OF SYMBOLS , I a (l/D}/(l/D) A flow area b s lot wi dth B llCtJlW o chord length c local skin friction coefficient with suction or injection average skin friction coefficient with suction or injection local baseline skin friction coefficient average baseline skin friction coefficient pressure coefficient suction flow coefficient - p v Ip V s s co IX) fuselage diameter D net drag with suction or injection DF friction drag on surface affected by suction or injection D baseline total drag o baseline fuselage drag baseline fuel load I F fuel load with drag reduction h slot height turbo-machine drag per unit flow rate (see page 37) line loss recovery factor length of suction or injection interval l. streamwise distance to first slot , lo overall length of fuselage lID baseline maximum lift-to-drag ratio I (lID) .

maximum lift-to-drag ratio with drag reduction

M Mach number N mass flow function (see page 66) P pressure q dynamic pressure r fuselage radius r rIc R baseline range I R range wtth drag reduction Ref Reynolds number based on fuselage length and free stream conditions Vs suction velocity V axial velocity w aircraft weight increment per unit surface area W mass flow rate

w w - F

e 0 W gross weight of aircraft o x' streamwise coordinate skin friction reduction parameter (see page 43) x normal coordinate y specific heat ratio -y bounda ry 1aye r th i ckne ss displacement thickness compressor efficiency turbine. effi~iency I momentum thickness slot injection parameter - p.V./p V J J OQ OQ

vi scos i ty suction parameter - C p V y/~ S Ql CD 00 p density Subscripts compressor conditions c j slot injection conditions s suction conditions turbine entrance conditions 2 turbine exit conditions 3 compressor exit conditions 4 compressor entrance conditions free stream conditions Superscripts (~) average values

* sonic conditions

III. PRELIM I NARY CONS I DERAT IONS A. Baseline Aircraft Drag - This study was conducted for typical CTOL cruise flight conditions and a fuselage shape representative of current long-haul subsonic transports. Most of the results of this study are pre- sented in terms of net drag reduction for the various schemes as a percent of a reference total drag D con-esponding to the selected baseline aircraft.

o For the present purpose 0 has been taken to correspond to the total drag of o a wide body transport (viz., a Boeing 747) cruising at an altitude of 11,000 m and M = 0.82. In order to estimate this parameter the following approxima-- ao tions were employed.

For the cited flight conditions the unit free stream Reynolds number is approximately 6.2 million/m so that, based on a fuselage length of approxi-

* 8

mately 67 meters, a fuselage Reynolds number, ReF,~n the order of 4 x 10 prevai ls. An average skin frictiori coefficient based on this Reynolds number can be obtained from the Prandtl-Schlichting correlation (Reference 6) yield-

**

ing -258 C • = 0.455 (log ReF) • = .00175 F I j.

Taking the diameter of the fuselage to be 6.7 meters the total wetted area is approximately 1400 m. Accordingly, OF ' the fuselage drag in the absence of any drag reduct i on effects is ,approxi ma£e ly 27,000 newtons.

An average skin friction coefficient for the wing is estimated to be given by the above skin friction law but for a length Reynolds number based *Characteristic dimensions of the various aircraft considered here are taken trom Reference (5).

**Compressibility effects would reduce this value by approximately 10% for the adiabatic wall case. However, this value is considered sufficiently accurate for the present purpose •

on an aver~ge chord length of 90 meters. This value (.00231) is applied to an exposed surface area of around 840 m • The skin friction drag of the wing is, therefore, 21,000 newtons. Adding 10% to account for skin friction on the empennage and engine pods and profile drag the total zero lift drag of the baseline aircraft is estimated to be 53,000 newtons.

The airplane cruises at maximum (LID). The d~ag corresponding to this condition is twice the zero lift drag. Thus, the cruise drag of the baseline aircraft, D , is estimated to be 106,000 newtons.

o .

B. Fuselage Geometry ~nd Pressure Distribution - As indicated earlier, calculations of the turbulent shear distribution on the fuselage in the pres- ence of tangential slot injection were carried out at the NASA Langley Re- search Center. The numerical finite difference technique due to Beckwith and Bushnell (Reference 7) was employed for this purpose.

In order to implement this methodology a body geometry and corresponding pressure distribution were ne~did. The fuselage was approximated by the quasi- ellipsoid of revolution depicted in Figure (1). In the absence of experimental data an estimate of the pressure distribution was made using the method of Reference (8). This is depicted by the solid line shown in the lower portion of Figure (1). Note that this distribution indicated the existence of sub- ambient static pressures over much of the fuselage surface as well as singu- larities at the fore and aft stagnation points.

To simplify the numerical procedures, the alternate pressure distribution shown by the dashed line was substituted with the agreement of the contract technical monitor.

c. Wing Geometry and Pressure Distribution - Accurate calculation of

the potential benefit of wing suction requires both three-dimensional tran- sonic inviscid analysis and three-dimensional laminar boundary layer analysis.

The latter should include the simultaneoUi efifects of suction and rapid - streanwis.e variations' in pressure as well as, possibly, stability considera- tions. Clearly, such a detailed approach would be beyond the scope of the present design study.

1:0 -- ..

<--_ _.

--..,.

! ! i !

I

'I

.8 - - --~ 2 9 O<x~lT

IT<x<lT lT~x~

DIS-TRI"BUTION /2

~ ! j , I j ! I

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9)~/2

(Sf

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PRES'SURE -2-)-,

- x X -

11 AND ( (11 x - -

-

55 i5

1... 55

: I

0 = = ~

.4,...6

){Re:ence

r r

r

xlL; .

-

FUSElACrr"f1EOt1ETRY x:: Alternat~ 1.

__

-

FIGURE , I I !

i I 1-"" I I

"~ .2___ -

------t--"

____ I o

o

-0.4 +1.2 +0.3 +0.4 +1.6 p r/L

c

== r co

To provide at least a rough estimate of the effect of suction on the baseline configuration a two-dimensional approach was adopted. Within this idealized framework the essential feature of a super-critical airfoil with the attendant weak shock was retained. In the absence of any direct informa- tion on the 747 airfoil the inviscid pressure distribution over a C-141 air- foil section, as obtained from Reference (9), was employed. This pressure distribution for both upper and lower surfaces is shown in Figure (2). It corresponds to flow at M = 0.76 and an angle of attack of 0.95°. These co va~ues are not precisely those of the baseline configuration, particularly th~ angle of attack. Nevertheless, the resulting pressure variation should.

be represent~tive in terms of the presence of'a normal shock on the upper surface.

The airfoil section geometry is shown in Figure (3).

1.6 1.4 " 1.2 1.0 PIP co .8 .6 Upper .It .• 2

o 20 60 100

Percent Chord FlGURE 2. PRESSURE DISTRIBUTION ON VING

'I t' I!.

\' ('"'I :":l ..

I

I I I

.~ J

£ l ..

T vic u~-' nA""" .v -.0225 -.0041 -.0058 -.0080 -.0109 -.0141 -.0201 -.0250 -.0311 -.0345 -.0356 -.0375 -.0398 -.0410 -.0424 ' -.0441 ..... -.0453 -.0449 -.0438 ~ -.0399 -.0369 -.0334 -.0307 -.0278 -.0180 -.0148 -.0114 -.0096 -.0039 -.0019 -.0178 ' -0.0029

I I

'I

Surface .

~ '.

.

Lower x/c .0017 .0217 .3560 .0009 .0031 .0059 .0099 .0165 .0373 .0681 .0936 .1038 .1242 .1547 .1750 .2053" .2557 .3059 .4058 .4554 .504R .5541 .6025 .6521' .6845 .7247 .7846 .8341 .8670 .8999 .9164 .9651 .9822 0.0005 ..

WINGGEOHETRY , 3.

vic 0688 ., .0059 .0073 .0084 .0131 .0154 .0213 .0252 .0343 .0408 .0492 .0589 .0630 .0659 .0678 .0678, .0659, .0630 .0591 .0485 .0329 .0182 .0 .0534 .0543 .0414 .0235 .0017 0·0042 ..

".0688 . , ..

, Surface FIGURE .

Upper 6962 .0008 .0013 .0018 .0053 .0076 .0112 .0233 .0480 .0728 .1478 .1979 .3480 .397Q .5470 .5965 .6461 ' x/c .0160 .0978 .1178 .2480 .2980 .4477 .7465 .7967 .8472 .8976 .9986 , , ,.~9?4 0.0003

--

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.

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IV. BOUNDARY LAYER CALCULATIONS A. Constant Pressure Laminar Results - Skin friction reduction due to uniform suction at constant pressure was estimated directly from the incom- pressible results given by Schlichting (Reference 6). These results are summarized in Figure (4). For the present application the parameter of !nterest is the net reduction in average skin friction coefficient, C , re- F lative to the baseline turbulent value, C •• The dependence of this ratio on F the relative suction rate C has been dedut~d from the results shown in Fig- s ure (4) and are presented in Figure (5) with the length Reynolds number as a- parameter.

Indicated in Figure (5) is a "cutoff" value of C = .00012. This value

s corresponds to the minimum needed to insure the maintenance of laminar flow as established by the stability considerations outlined in Chapter XVI I of Reference (6).

Finally, we note that these incompressible results should be reasonably accurate for the present high speed application since only the ratio of skin friction levels is involved.

B. Laminar Results with Pressure Gradient - The analytical method uti- lized for these calculations is described in detail in Appendix A. It em- pl6ys the momentum integral technique due to Torda (Reference 10) in conjunc- tion with Thwaites method (Reference 11) to permit initiation of the calcula- tion at a stagnation point.

The numerical computation scheme based on this method can be exercised in two distinct ways. The more general option accepts arbitrary distributions of suction (or blowing) and pressure gradient and determines all boundary layer characteristics. The alternate option imposes the condition that the boundary layer thickness is constant. In this case, for an arbitrary variation of ex- ternal pressure, the computation yields the requisite suction distribution as we,ll as the corresponding variation of all other boundary layer properties.

i Th!e latter option is useful in terms of providing a mechanism by which, in an approximate sense, the preservation of a laminar flow can be assured.

.10~.----------------------------------------------------~

C x 10 = 10

s .01 C f

- -=._------

-- =-- - ---' .5 .001 .

. 000 1'----""----~--"""'-..a.-"""'- _ ___':.__ __ __'_ __ ..a._...&._..a._ __ ___''__''_~ __ ~ ..........

6 7 10 10 10 10 Reynolds Number

FIGURE 4. DRAG COEFFICIENT FOR FLAT PLATE WITH UNIFORM SUCTION

" .

3~------------------------------------------~--~

Reynolds Number = 1.0 ~Hinimum C, t for Laminar ·C IC

F f'i

i .1 L-~ ________ L- ____ ~ __ ~ __ ~ __ ~~~~~----------L-~--~ .001 .0001 FIGURE 5. REDUCED SKIN FRICTION COEFFICIENT WITH SUCTION lit

In applying this analysis to the: baseline wing configuration the follow- ing objectives prevai led; ~he suction distribution should insure that the state of the boundary layer remain laminar; the suction distribution should prevent separation under the influence of the inviscid pressure distribu~ tion associated with the baseline configuration; the suction distribution should yield the minimum skin friction consistent with the previous require- ments. Toward this end the suction distributions on the wing were determined as follows.

In regions of constant pressure and in regions of favorable pressure gradient (which tends to suppress the rate of'g,rowth of the boundary laye"), the relative suction rate was maintained constant at the optimum value

C = .00012. In principle, this can be expected to preserve the laminar

s boundary layer state. In regions of adverse pressure gradient the variation of C was computed by requiring that the boundary layer thickness remain con- s stant at the value associated with the start of the pressure rise. The cor- responding momentum thickness is found to decrease through this region so that, here again, it can be anticipated that the laminar state will prevail.

The results of these calculations are shown in Figures (6) and (7). As can be seen, very modest increases of suction over the optimum value are re- qui red to prevent separation on the lower surface of the wing. On the upper surfac~, of course, a very large "spike" of suction intensity is needed at the 70% chord station and at the trailing edge to maintain an attached laminar flow. Note, however, that although the maximum value of C is on the order of s 40 times the optimum rate it is still less than .1% of the unit free stream flow rate.

The corresponding distribution of skin friction is shoWh in Figure (7).

These laminar distributions have been compared with turbulent estimates made ~sing the method described in Reference (12). Note" that for the upper surface, separation is predicted at the 70% station and that the turbulent shear is assumed to be vanishingly small thereafter.

The pertinent results needed for the performance calculations are the net reduction in average shear for the entire wing and the average suction rate.

. 004 ~------------~~--------------------~ Uppe~ Surface ~ (

I I

.003 ----i-.------.i-.-.-- .. -.----l--- ..

. i I I t

, i : I

i I I

I

I I . .. --~_.- - ..

-. l .... ·.-- .. ·.-_·_·· ----- .......... L ..

. 002 I j I , C f s

I I

. _. __ .1_~_ ... _

.001 --- :l-----t---- -- ..

----=--~

o

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.001 I

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Lower Surface

I

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i

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.~.

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o

•

I

o .2 .4 .6 .8 1.0

x/c CHORDWISE VARIATION OF SUCTION PARAMETER ON WING SURFACES FIGURE 6.

1'.0 .8 .6 Surface SURFACES Lower .4 \-/ING Turbulent ON .2 FRICTION SKIN o LOCAL x/c OF .

rl 1.0 VARIATION .8 Separation CHORD"/ISE .6 7.

fh Surface - wi .4 FIGURE, nar Upper Suction-- Turbulent Lami .2

o

0' f .001 .003 .• .004. C .....

These data have been computed from the above results and are summarized be- low in Table I. The results indicate that the wall shear is reduced to ap- proximately 25% of the turbulent values by application of suction at a rate on the order of twice the optimum value for a flat plate.

TABLE I SUMMARY OF VISCOUS DRAG REDUCTION RESULTS ON WING Upper Lower Total Surface Surface Wing Average turbulent shear .00175 .00283 .00229 CF• I Average laminar shearC .000575 .000375 .000475 F .343 .133 .238 CF/C .

F I suction parameter C Average .000375 .000185 .00028 s C. Turbulent Results With Slot Injection - Turbulent boundary layer so- l!utions with tangential slot injection were obtained by F. G. Howard at the

*

NASA Langley Research Center. These were carried out for the fuselage con- figurations previously shown in Figure (1). The first slot is located at x/L = 1/11 and subsequent slots are placed at intervals of ~x/L = 1/11, u, o 0 to a maximum of 10 slots.

The assumed surface pressure distribution up to the first slot is shown in Figure (8); from the fi rst slot to the end of the fuse'lage the pressure co- ~fficient was assumed constant and equal to zero. The nu~erical method of Reference (14) was used to calculate the boundary layer characteristics up to the first slot, assuming a fully developed turbulent boundary layer from the *A more complete presentation of these results may be found in Reference (13).

h- 7.62 cm y, em Initial Velocity Profile 1.0

o :5

c

p Location of First Slot I

I

- - -...:- --'

Pressure Distribution t -0.2L-----------------~----------------~ o .05 0.1 x/Lo FIGURE 8. INITIAL VELOCITY PROFILE AT FIRST SLOT AND PRESSURE VARIATION TO FIRST SLOT

nose. The boundary layer thickness just upstream of the first slot is ';~

o = 3.6 em, the displacement thickness is a = .57 cm, and the momentum

thi~~ness is e = .35 cm. The boundgry layer velocity profile was then com-

bined with estimated slot exit velocity profiles having a shape similar to those measured in Reference (15), and an average Mach number of M. = 0.2.

J The resultant complete velocity profile was used as input for the slot in- jection code of Reference (7). The resultant velocity profile at the first

slot (for h = 7• .62 cm) is shown in Figure (8). The slot to free stream to-

tal temperature ratio was assumed constant and equal to 0.9895. The varia- tion of skin friction and velocity profiles downstream of a.single slot is· indicated in Figure (9).

The numerical finite-difference solution of Reference (7) was modified so that the effect of multiple slot injection on the fuselage skin friction could be determined. The local skin friction coef:icients (C ) obtained f downstream of one, three, five and ten slots (slot height (h) ,of 7.62 em) are compared with the local skin friction coefficient on the fuselage with- out slots in Figure (10). The local skin friction reduction with only one slot is significant when compared to that without slot injection. The bene- ficial effect of the slot injection is most pronounced immediately downstream of the slot exit and diminishes with increasing distance downstream from the j.

slot; this occurs because in the near slot region the wall friction is influ- enced only by the slot flow while further downstream mixing between the high momentum boundary layer flow and the relatively low momentum slot flow in- creases the wall shear. The effect of slot height on skin friction varia- tions with downstream distance is demC":,')trated in Figure (11) for the ten slot case. For these calculations the slot velocity profiles were scaled by the i slot height so that the slot mass flow varied in proporti,onto slot height.

. .1

As in the case of the laminar results, the net reduction in average skin fricti~n relative to the baseline value, CF/C ., is needed for the performance F calculations. For this pur.pose the average wa\l shear of the fuselage was estimated from the data shown in Figures (10) and (11) and normalized with respect to the corre~pondihg average for the no slot case. The resulting variation with number of slots and slot height is presented in Figure (12).

X' ,.-.

) A .

_ I' OF ,,;: -Va:> » I I ' .

, ; , 7 , ; J DOWNSTR£AM } 40 .1.1' , BEHAVIOR FRICTION Profiles x/h ..

SKIN _._

v

...

AND Velocity

"----

Prediction ....

I

·

..

L DEVElOPt1ENT

NGLE-SCof---·

VELOCITY Finite-Difference y _..... S I ..

FIGURE~.

.2 • 1 .4 .8 .6 1.0 I f C Cf· .

N

!

0.338

J

OK __ '"!.

___

max

---

--

0.9 _______

----

- cm,(V/V) .0.:8

------

_________ -.l!.~_II_~ - 7.62 ;._;.". __ H =

---

h 0.7 -

__

..--

--

I I

__________ 0.6 ._.

o INJECTION,

J

x/L ____ ~--

I

SLOT 0.5

~~ I

\.JITH ~---_-- .If Slots

1._

o

_ .,// Case REDUCTION 0.3

I L _ I

Slot" <2.!-

,.-

1 S "No /' 0.2. FRICTION SKIN

I I

I I I I I I I I I

·1

.I

.0.

10.

o FIGURE .000 .000 .001 .0016 .0020 .0024 f C .., ' ...

~ N N

.002

h = 3.81 em

.0015 .0010 .0005 or---~----~-----'--~--~----------------+----------

h = 7.62 em

,0015 .0010 .0005

h = 15.2 em

.0010 .0005 50 100 150 x/L o FIGURE 11. VARIATION OF LOCAL SKIN FRICTION ON FUSELAGE WITH SLOT

INJECTION; M. = ,0.2 23

J

o

VENES.S.AS.A_EUNCIIOtL EFFECT!

ON Slots of SLOTS 4 - Number OF 'CT-IONREDUCTil 0.2 7;.62 3.81 NUMBER

15.24 =

h,cm J SKIN--FR OF M.

0 0 GURE-l2-.· I

t-

I

o

F .8 .6 Fi CF'C ..

~ .

N .z::-

of height, both slot and increasing slots additional with improvement The is clear from It is apparent.

mass flow, to increasing correspond which are available drag in viscous (~ 50%) reductions that large Figure (12) systems.

injection use of slot the through the skin that and (12).suggest (11) Figures (10), shown in results The of injection ihe numbe~ i~cr~asi~g ~y is' improved reduction friction One probable spacing).

slot (for constant rate a diminishing but at slots the present for very important; is slot locatlon is that for this reason most rearward and the effective is the most slot most forward the st,udy, in slot location a forward of Two advantages effective.

the least slot is high and level is friction skin the no injection are (1) study the present friction local skin for effectiveness thin; slot layer is boundary (2) the to slot thickness layer of boundary low ratios at is improved reduction an obvious offers injection Forward slot and ,17).

(References height area a larger over occurs drag reduction in that the advantage additional the when is illustrated location of slot This effect the aircraft.

of' ten case of the (12) ; consider from Fi gure is made comparison following 7.62 cm

with h =

five slots case of wi th the em compared

= 3.81

with h slots the AI though position).

the same is located at case in each fi rst slot (t~e for the that be the same as would larger slots the five flow from mass total five for the 27% greater is reduction skin friction slots, the 3.81 em ten 12).

in Figure (see comparison slots than for the ten configuration slot The investigated.

also been number has Mach of injection The effect in slot variations includes (13), which Figure in are summarized results the of that reductioh It appears number.

Mach as injection as well height friction in the skin reduction further provide number can Mach i~jection 13).

Figure A and B'in Foints (i.e., compare flow total mass the same fdr in- are drag penalties substantial seen subsequently, will be as However, its and reducing mass flow required the of capturing the process curred,in The total slot locations.

at the level desired to the Mach number average the last of downstream is captured the slots through all injected flow m~ss j due to However, and reprocessed.

design, baseline the proposed slot, in of each downstream layer boundary the fuselage occurs in which' the mixing energy The excess than desired.

energetic flow is more captured the slot,

o'f·· No.

C Slots h,m w. C';'C Fi . J F 0'.2 .00110 .63 10 .0381 .000784 .45 10 .0762 0.2 10! .000411 .24 .1524 0.2 ~ .00119 .68 O! 1 10' ~0381 I· . ~ .00098 .56 10 .0762

o 1

.00135 .77 .0381 0 : 1 5 .00118 .67 .0762 O. 1 5 t !

1.0 Number of Slots .6 .4 .2 .

O~----------~----------~----------~-----------J .2 .05 • 1 .15

o

h,m FIGURE 13. SKIN FRICTION REDUCTiON EFFECTIVENESS AS A FUNCTION OF SLOT HEIGHT AND INJECTION MACH NUMBER

is removed in the turbo-machinery used for pumping the injected flow, which will be discussed subsequently, This problem is aggravated by reduction of the slot height, which increases the mixing and energization processes, as indicated by the velocity profiles at a station near the end of the fuselage shown in Figure (14), a"nd by reduction of the injection Mach number.

20 ~-----------------------------------1

h, em ~

~~ ____

-=~~ ____

~~ __

~ ____

o ~ ____

1.0

o

V/V CD OF FUSELAGE; AT END PROFILES 14. VELOCITY FIGURE Ii. = O. 2 LOTS HI TU lOS J

. ' . V. DRAG REDUCTION RESULTS A. Fuselage Slotlnject:ion - The scheme for uti 1 izing the drag reduc- tion potential of slot injection on the fuselage in conjunction with a turbine/compressor illustrated in Figure (15). The turbine processes the boundary layer air at the end of the series of slots and returns the ai~ through an annular duct around the fuselage from which it is injected to the slots. Since the flow is injected at a low velocity in order to reduce skin friction, there is a drag associated with the turbine flow. The, power gen- erated by the turbine is absorbed by the compressor which also processes boundary layer air. The compressor air is discharged at a high velocity pro- ducing thrust which partly offsets the drag of the turbine flow.

As noted in Figure (15) there are two ways in which the boundary layer air can be processed. In the first way, the compressor can handle the "inner" or lower velocity flow near the surface whi le ,the 'turbine handles the "outerl,1 or high velocity flow. Alternately, the location of turbine and compressor are reversed, with the turbine handl ing the"inner" flow and the compressor handling the "outer" flow. The arrangement which would be selected is the one giving the smallest net drag when processing the boundary layer air pro- duced by the injection.

From the veloci ty profi le data such as those presented in Figure (14), the average velocity as a function of boundary layer flow can be determined.

Here,' the average velocity means the average "momentum" velocity defined by ~ 1 V = - fVdW W wh:ich is judged to be the most pertinent average for use in calculating the dr:ag of the turbo-mach i ne flows. For conven i ence of app 1i cat ion, the average ve'locity is determined as a function of W/\L, the boundary layer flow with J respect to the injected flow,W. being the total flow injected from all the J slots. The results are presen~ed in Figures (16a) and (16b).

The average velocity enters into the drag calculation of the turbo- machines in a straightforward manner. The drag of the turbine flow is given

Initial Boundary Layer

v

Final Boundary Layer Turb.

Camp.

V or V ~

j 2 '" ;

·

Ii Skin !i ~

·

...

i F ~ (a) Compressor Handling Inner Flow ti Ii I!

"

·

M l' { V3 ~ " Camp.

-

l i p " Turb.

~.

:

I

i..,p (b) Turbine Handl ing Inner Flow FIGURE 15. SCIfEHATIC OF SLOT INJECTION SYSTEt1 -.~ :-

-' -

250~------------------------------------------' h, :m .

.

V, m/s

. 0 W/W.

J FIGURE 16a. AVERAGE VELOCITY IN BOUNDARY LAYER AT END OF

SLOTS; .M. = 0.2

J I •

180~ __ ------------------,--------------------------------~

V, m/s

j '0 .• 5 1.0 2.0 1.5 2.5' w/w.

J

FIGURE 16b. AVERAGE VELOCITY IN BOUNDARY LAYER AT END OF SLOTS; M. = 0.1

J - j~

by by the handiled layer flow boundary in the velocity is the average where V velocity.

slot injection or the velocity the discharge V is turbine and discharge and at intake the pressures that drag implies of This formulation the boundary premise of a basic pressure), stream to free same (equal are the .

case.

in the real true is very nearly which layer calculations turbine performs work Which V ' the from V to velocity the In reducing to in- the work utilizes The compressor compressor.

to the is transmitted V to the value the intake handles from flow it of the the velocity crease 4 in a thrust results flow the compressor this case, V . In value discharge by given ) (V - V thrust == Wc compressor by the handled layer rlow boundary of the velocity is the average where V compressor.

given by is then drag turbo-machine The combined

= WtI

drag turbo-machine where W (V V - (....£.)

I = V -

W 3 1 2 t given for a Then, V ar.e known.

V , V and the quantities application, In which of a calculation by means found of V3 can be the value Wc(W , value ?f t compressor of the input to the power the turbtne of power output equates the flow whi ch of the energy an increased input to the power transforms and then V3" velocity discharge increased to an is converted tur- conventional of power, conversion and the production formulating In losses ducting In addition, are included.

efficiencies and compressor bine of or ratio factor (recovery loss factor of a by means into account are taken

total pressures) which accounts for the entire loss in the ducting, both ahead of and behind the machines. The loss factor is especially important ~l in the case of the turbine because of the turning of the flow and the long li ~. I duct length upstream for injection through the slots.

To convert the average velocity data of Figure (16) to values of aver- age velocity for the turbine and compressor, it is necessary to fix the re- }; i' spective flows. For the turbine, the flow is fixed ~ priori since it is li . .,,;'" equal to the injected flow. However, the compressor flow may be chosen arbitrari ly witH the final choLce deferred until the effect ,on jet drag re- .

~

-.

duction is determillt;Q. In the case where the compressor flow is the "inner" flow (see Figure 15) the average velocity V for a given value of Wc/\~t is s.

; ~~ the value of V read at \~N. = W /W. Then, since the turbine flow is the J c t ", same as \"j' the turbine flow extends from W/\~j = Wc/Wt to W/W = 1 + Wc/W , j t f , The average velocity for this portion of the boundary layer flow is given by « , " . !

~

where V 1 is the va I ue of V at ~1/\~j = + W /~I and ,V2 is the va I ue of V at

" c t - ~, \UW. = \1 /W .

t J c #

, t

The average velocities for this case are shown in Figures (17a) and (17b) - as a function of Wc/It/ .

!

t .

" ,- In the case where the turbine flow is the "inner" flow, the average ve- ,

k

'

loeity V is determined as the value of V at W/W = 1. For a given value of ~

.

1 j

Wc/\/t' the compressor flow extends from W/\~j = 1 to \UWj = 1 + W /W and its

c t " average velocity is given by .,~-~ .

(1 + W /W ) V - V

2 c t 1

V = ~I/W

c t where V

is the value of V at \oI/Wj = 1 and V is the value of V at W/W =

l 2 j The average velocities for this case are shown in Figures (lBa) and + W/W • t ....

(18b).

,~ .......

"'t , .. ~->:

200~--+-------------------------~----------------------~ Turbine ~,m Compressor .2 .4 .6 1.0 ' .8 .1.2 ),J !v.

c t AVERAGE VELOC ITI ES WI TH COMPRESSOR HANDLI NG ;'1 NNER" FLOW OF

BOUNDARY LAYER; M. = 0.2

J " i _

Ii 1\ '\."

.

( .

r J' \ ,."

'i it ;:' ~i: 200r---~------------------------------------------------~ " Ie .~

j

)~ Turbine

~

..

ij

h,m ~ " ~ .. ~ \: 1; J' " \,;.:l '''":: Compressor Ii ~ H ".ljI: t' I' "Q,ii , ~, ~ ~rJ " !: ~ . 140

"'

".J'

~t: ~ :r, ,~t

~120~------~--------~--------~------~--------~------~ 1

0,

.2 .4 .6 .8 1.0

1 . 2

!~-,; Wc/Wt ~ t .....

AVERAGE VELOC IT I ES WITH COMPRESSOR HANDLI NG FIGURE 17b. INNER FLOW; M ,,:O.1

J

Cl

" ...., "

-

.

.r

200~----------------------------------~----------------~ Compressor h,m .0381 Turbine .0381 ~ .0 62 . 1524' ) 120 ____ 0--I
ooo_ ____ ..... _____ ...r.. _____ ...... ________ ---' "0 1.0 1.2 .~ .6 .8

w /w

c t FIGURE, 18a. AVERAGE VELOCITIES WITH TURBINE HANDLING 'INNER' FLO\J OF BOUNDARY LAYER; M ~ 0.2 j " I , 1 •

'j', I,;, J' i , ~ " .

v~, m/s Compressor h,m ..

, .0381 J ~ i .0762 , Turbine , .0381 , r-- .0762 ..

, ~', -, ,.

I I I' I

>

.2 .4

o .8 1.0 1.2

, ..

FIGURE 18b. AVERAGE VELOCITIES WITH TURBINE HANDLING INNER FLOW; M.=O.l J .'

I •

Consider now an airplane with a baseline total drag 0 and fuselage friction drag OF' \.Jith injection, the fuselage drag becomes o where X is a factor representing the effect of injection on skin friction.

The net drag of the airplane with the injection system, including the reduction in skin friction, the drag due to the turbine and the thrust due to the compressor, i; given by_

° = ° - (1 - X) OF + W.I

o 0 J The injection flow produces a reduced skin friction drag, defined by the , factor CF/C ., over the portion of the fuselage i~fluenced by the slots.

F The value of'X is not exactly the same as CF/C . because injection starts F , at some distance from the nose of the fuselage so that there is a small por- tion of the. fuselage where the drag remains unchanged. In this region assume that the friction coefficient varies inversely with distance to the 115 power and that the wetted area is proportional to the length. Then the value of X is gi ven by (L:/L)·8

X = CF/C . + (1 - CF/e .)

, 0 F F , , where L. distance to first slot I.

L length of fuselage.

o Application of these results to the baseline configuration is made assum- ing the slots to extend completely around the periphery of the fuselage. For the cases which were examined the flow rates \oJ. are J

H. h, m W. , kg/s No. of Slots J J 10 0.2 .0381 1156 0.2 .0762 10 312 10 0.2 .1524 624 10 0.1 .0381 78 0.1 10 .0762 156 0.1 .0381 O. 1 .0762 78 The results, which are presented as curves of % (net drag with in- o ject ion/drag wi thout inject ion) vs. \-1 /W (compressor flow/turb i ne or i n- ~ c t j~ction flow) for various values of k1 (line loss factor of injection flow), are based on turbine and compressor efficiencies equal to 0.9. This would tend to give results which are slightly optimistic. In the same spirit, the line loss factor of the compressor flow was taken to be unity.

Results for the largest slot height considered (h = 15.24 cm) are given

in Figures (19a) and (19b) for the compressor handling the "inner" and "outer" flows, respectively. Note that the figure includes a line representing the effect of injec;tion on skin friction only, given by In addition, a line representing results without the turbine/compressor ef- fect is included. This is given by } !

I ",J

1.6 .,;"'''' / .

.,;'" /, , /'" 1.5 f-- /' /' .

,/ /' .

Lit /<.

f-- \~i thout Turbine/Compress~r .

/' .

/"

./' . k .

V"""" 1

1.3 ~ q

-

-

DID o .95 f- 1.2 .

1.0

1 . 1

, .

--

, I 1 .0

-

.

.

) I-- .9 Skin Friction Only ~

L

-

i -

-

·1 .

I J

J 1

,8 , o .2 .It .6 .8 1.0 1.2 ~ \J /\J c t I' FIGURE 19a.

NET DRAr, UJTH SLOT INJECTION, COt~PRESSOR HANDLING INNER I FLOW; h = 15.2~ em, M. = 0.2 lt1 J

1.4 , , Turbine/Compressor

£With=-

, 1.3 --- ------

~,- - -

-

- -

= .9- k1 .

. 95 1.2

-

.

0/0 o 1.0 1.1 f-- .

.

1.0

-

-

.

f ~ .9

Skin Friction Only

.

'"

-

~,

r

I:

-

- -

"' ..

I J I I

, .8 I

~\.

.4 .6 .8 1.q 1.2 o .2 f.

"

~t W.lW L t p. ¥ ,

"

:i{ ... J< FIGURE 19b. NET DRAG WITH SLOT INJECTION, TURBINE HANDLING INNER FLOW; h = 15.24 em, M. = 0.2 ... " J ·z ~ t~ --> "

:t

-

" ; .~~ , , ~{ < ..

: 'i11d

It is apparent that the turbine/compressor is quite effective in reducing net drag although not to an extent sufficient to produce a positive result (0/0 less than unity). Comparison of the results given in Figures (19a) o and (19b) also indicates that slightly better results can be achteved with the turbine processing the lower momentum "inner" flow and that in neither case is the compressor flow of critical importance. These trends prevailed for all of the configurations examined.

Additional results for the smaller slot heights are presented in Fig- ures (20) and (21). Furthermore, to demonstrate the basic soundness of the concept of having the turbo-machines process boundary layer flow, some cal- culations were made with the machines handling free stream flow (V = V = V ).

oo 1 4 The comparison Sh(Mh in Figure (22) demonstrates the potential benefits.

Comparison of the results shown in Figures (20) and (21) with those pre- sented in Figure (19) in'dicates that the smallest slot height, despite its inferiority in terms of reducing viscous drag, gives the best net perfor- mance. This is, of course, a reflection of the large penalty in momentum drag which increases directly with total injector flow rate and, therefore, with slot height and/or injectibn Mach number. It should be noted also that the effect of the loss factor kl is greatest for the largest slot height and decreases systematically with decreasing height. This is, again, an indlca- tion of the large penalty in drag associated with increased flow rates.

As can be seen in Figure (21), even for a loss-free system (k = 1), net drag reduction is not attainable with M = 0.2. Accordingly, additional j

calculations at a lower jet Mach number (M = 0.1) were carried out for the

j small and intermediate slot heights. These results are presented in Figures (i3) and (24). Again, even with the decreased effectiveness of slot injec- tion in reducing wall shear (c.f. Figure 13) some improvement in overall performance is attained due to the lower mass flow rates involved.

Although the results shown in Figures (23) and (24) indicate some net drag reduction the actual values are quite small amounting to only 1 or 2% fo~ realistic values of line loss factors. Further reduction in jet Mach

, .

: r 1.3 : 1 0r:,'" .

--'

--

--

- I,

~~

----

1.2 f-- Without Turbine/Compressor

---

.

--- 'I:

~--

k .9 .95 t-- 1.1 1 n DID o .

~ 1.0 ~ .

Skin Friction Only I-- . .9 - ,

- ~

I I

'f I I

1 I

., .

.8 / ..

0 .2 .4 .6 . 8 1.0 1.2

.. J

\I /\1 c t ,~ FI'GURE 20a. NET DRAG \~ITH SLOT INJECTION, COHPRESSOR HANDLING 'INNER FLOW; h = 7:62 cm, H. = 0.2 .,,, J ; t " ~ .• ~.,. ~I ,: } ,~ '1:!-" f, :-i ~';

]

-'<:~:,"J .1 :~ ~: } .

om ...t.-:J5

1.3 ..

~ ~ Wi thou t Tu rb i ne/Compressor f--, 1.2 -- 1--- -- ----

- -

k .9 = .95 1.1 ~

-

1.0 DID '0 .

1.0 i- .

Friction Only

(Skin

I-- .9

- -

, I

I I I

I

I

.8 1.2 1.0 .6 .8 .2 .4

o

\1 1\1 e t ) INNER NET DRAG WITH SLOT INJECTION, TURBINE HANDLING FIGURE 20b.

FLOW; h = 7.62 em, M. = 0.2 J

- .'

" .'

1.2 ~ J\lithout Turbine/Compressor .

--

--

~ -~ ~ kl

-'-

DID

-

o

--

1 n

--

1.0 I-- Only Ski n Friction

- - -

.

.

I f I I

I

.8 1 .2 ' .8 1.0 o .2 .4 .6 W 1\01 c t FIGURE 21a. NET DRAG WITH SLOT INJECTION, COMPRESSOR'HANDLING INNER FLOW; h = 3.81 em, M. = 0.2 ;J " , • " I ,

1.2~---------------------------------------------------------.

1. H-- I--

--

---

DID

-=

1.0

Of- 1.

1--_--4rt-_Sk:. F r jet i on On 1 y

9-

I I

I I I

o 1.0 1.2 .6 .8 o .2 .4 \1 I'.J e t FIGURE 21b. NET DRAG WITH SLOT INJECTION, TURBINE HANDLING INNER FLO'.,,; h = 3.81 em, M. = 0.2 J

1.6~------~-------------------------------------------' h,cm "~4 1.5

~---~-_I

Using Free Stream Flow ........ __ ....... .

Using Boundary Layer Flow 1.4 1.3 7.62 15.24 1.2

---

-----

- --

3.81 1.1

--- -- --

---

--

--

--

1.2 1.0 .4 .6 .8 . .2 \~ I\~ c t I FIGURE 22. COMPARISON OF NET DRAG WITH TURBINE/COt~PRESSOR USING FREE STREAM FLo\·/ AND BOUNDARY LAYER FLOW; M. = 0.2 J

h = 7.62 em 1.2 Without Turbine/Compressor 1.1 r-

--

--

-

-

J-

I---

-

0/0 = .9 kl o qr:; 1.0 10- 1 n

-

-

- -

H-- .9

L Skin

Fr i et ion Only

I I

I I I

.8 h == 3.81 em 1.1

---

1.0 I-- 1 n 0/0 o I-----w-.-- - ---------

----------------*

Lkin Fretion Only

I I I

I I

.8 0 .2 .It .6 .8 1.0 1.2 \-I /\J e t FIGURE 23. NET DRAG 1./ I nl COf1PRESSOR 11ANDll NG INNER FLo\l i 11. = O. 1 J

....

h = 7.62 em

.

1.1 , ~/ithout Turbine/Compressor J

t-- - -

L kl :::: .9 ~ .

• !)5 --: '1.0 1 n , 0/0 o

-

-

I"'- -

.9 , ..

'~Skin Friction Only

I I I I J

.3 , :\ - 3.31 em h 1.1 " Turbine/Compressor .~\~ithout

1.0 I-- kl = .9

1.0 ~ ..

DID ......

o

-

---

-

-

lSkin ".9 Fri ct ion Only .

.

}

I I I I I

.. 8 .2 .4 .6 .8 1.0 1.2 \I /\-1 c t FIGURE 24. NET DRAG '·/ITH TURBINE HANDLING INNER H. 0.1

=

FLO\"i J " I

-r

i

number, or injector flow rate in general, is not likely to provide signifi- cant improvement since the wall shear ratio would approach unity. This ef- fect is demonstrated in Figure (25) in which the curve of DID versus M.

o J goes through unity at H. + O.

J In summary, these results indicate that the baseline design, which makes exclusive use of multiple slot injection and captures the required mass for injection downstream of the last slot, will provide, at best, marginal drag reduction. It appears that alternate schemes are needed, possibly combining slot injection with other drag reduction methods, to provide significant improvement in performance. Several alternate schemes are examined in the subsequent sections; however the considered schemes do not encompass all pos- siblities by any means.

B. Combined Fuselage Suction and Slot Injection - This scheme consists of a passive system requiring no pumping or turbo-machinery. The system depends for its operation on the pressure difference which exists between tne upper and lower surfaces of the fuselage at a small angle of attack. The high pressure lower surface is composed of a porous or slotted surface through w~ich suction takes place. The flow is ducted to the ,top surface of the fuse- l?ge where it is discharged. by slot injection. The physical arrangement would consist of a series of 10 suction surfaces encompassing the lower half of the, fuselage, each of 6.1 m length. At the end of each section, the suc- ,tion flow is collected and discharged through a slot on the top of the fuse- lage, thus comprising a system of 10 slots at 6.1 m intervals.

As indicated in Figure (5) suction at an excessive rate can produce an increase in skin friction rather than a decrease. The largest drag reduc- tion is obtained with the "optimum rate" corresponding to the stability limit for sustaining a laminar boundary layer.

The injection at low velocity on the top of the fuselage produces a re- duction in skin friction. With the flow fixed by the suction requirement, the question arises about the best way to distribute the flow on the top of

I , I

. 1

1 i \ -.1 DID o 1.00 ... ;.

.96 • 1 .2 M.

i J 1.

.' J d ~

.J

FI~URE 25. EFFECT OF INJECTION MACH NUMBER ON NET DRA~; h = 3.81 em .

i j

n

'~J

the fuselage. The same flow may be injected with a larger slot height by limiting the peripheral extent of the slot. The skin friction reduction increases as slot height increases, but the extent of surface affected by inj~ction decreases. The best slot height is the one which gives the ~o!: .

greatest net gain from the two opposing effects.

The following simple analysis shows that the best slot height is the sm~llest slot height; that is, the flow should be distributed over the largest possible lateral extent of surface area. For a given injection flow, W, the slot height h and the slot lateral extent b are related by

w ::; p. V. hb

J J For the length of the slot coverage L, the area of surface affected by in- jection is bL. The friction drag on this surface is given by where CF/e • is the reduced skin friction factor due to injection.

F I The drag reduction is then given by

60F = (1 - CF/C .) C . qoo bL

F F I I which may also be written

(1 ~ c IC ) C . qoo LW

F F F.

I I

60 F = ------;-:---;---'----

p. V. h JJ Since C ., q , L, W, p. and V. are all constant, the drag reduction is written F I 00 J J (1 - CF/C .)

F

60F::; constant -< - '-h=-----...;..I-

It is apparent that the maximum drag reduction is obtained when the value of (1 CF/CF.)/h is a maximum. The data in Figure (13) are converted to this I

., expression with results presented in Figure (26) showing that the largest drag reduction corresponds to the smallest slot height.

The suction surfaces are arranged in 10 sections of 6.1 m length on the bottom half of the fuselage. At the end of each section, the suction flow is collected and ducted around the fuselage along which it is injected in a slot encompassing the top half of the fuselage. Thus, the slot injection consists of 10 slots at 6,1 m interv;ds. This arrangement does not present serious difficulties with regard to internal ducting, especially in view of the low flow rates characteristic of suction requirements. It is estimated th:at with a 1/2 inch gap around the bottom of the fuselage, the suction flow of each 6.1 m section can be handled with a pressure drop of one-half of one percent. Including the ducting loss and the required velocity head for injecting the flow through the slot on the upper half of the fuselage, the ; tqtal pressure drop wi 11 be around 4 or 5 percent. Such a pressure differen- " , tial between the lower and upper part of the fuselage can be obtained with a small angle of attack.

The flow through the suction surface is , , 'lTd W=C p V -L s co 00 2 and the flow through the injection slot is

W = A p V 'lTd h

co 100 2 Hence, the slot height is gtven by

h = C L

s The value of C determines the skin friction reduction factor due to suction s and the value of h determines the skin friction reduction factor (€F/CF. ) . I S due to injection (CF/C .) .. It should be noted that in order to determine F I J (CF/C .) , it is necessary to fix a Reynolds number. The value used in the F I s

• I .~ 15~------------------------------------------~ .10 Number M. of Slots, J • 1 • 1 5 OL-------------~--------------~------------~ . 15 .05 .10 -0 PARAMETER DESCRIBING DRAG REDUCTION AS A FIGURE 26.

FUNCTION OF SLOT HEIGHT < " f •

Ii ~ \;

J

.

present application is 10 , roughly corresponding to the average fuselage length.

; I.

" The drag reduction due to suction is given by I; and that due to injection is

t.0 = (1 - (CF/e .) ) c • qex> ~d L

F F J I • I J the drag increase due to the momentum change of the flow is given by

t.O = w (V - V.)

m ex> J which in terms of the suction flow coefficient is written

t.O = 2C q TId L (1 - V./V )

·m s ex> 2 J ex> If it is assumed that the injection density is the same as the free stream density (which is very nearly true) then the velocity ratio is the same as the injection flow parameter

V./V = A

J ex> The net drag reduction is given by

t.O = t.D + t.D. - t.D

s J m The original skin friction drag without suction or injection, determined by both the upper and lower halves of the fuselage is given by Hence, t.O

OF. =

I

The values of ~/DF. determined as a function of the suction flow co- efficient.,5s are shown In Figure (27), calculated with C . = .00175 and F

A = .244." The figure shows the contribution of each of ~he three compo~

nents of drag, indicating that suction contributes the largest part of the drag reduc t ion.

In order to evaluate the effect of drag reduction on airplane perfor- mance, it is necessary to establish the drpg reduction with respect to the drag was overall drag. In the application treated earlier, the overall This

established as equal to four times the fuselage drag or D = 4

x DF .

o .0 • so, I tiS relationship will also be used here. However, in order to do necessary to establish the realtionship between DF and D ..

F o I As in the earlier application, it is assumed that there is an initial fuselage length of 6.1 m which is not treated by ~uction or injection. The diag D . excludes this length since it represents the original drag on that F I portion of the fuselage treated with suction or injection. Adopting the same assumptions used before (turbulent skin friction coefficient varying inversely with distance to a .2 power and surface area varying directly with distance), the relationship between D . and DF is d~termined as F I 0 .8 D F. L.

I (-')

1 - --=

L DF Wi th L. = 6. 1 m and L = 67 m, I 0 ~F.

, --= .853 DF The net drag is found from

*This corresponds to slot injection at M = 0~2. All performance estimates

j

for this scheme are made using (CF/e .> values corresponding to M = 0.2

F j since this provides greater reduction'in wall shear than the M. = 0.1 case.

J

.6 __ ---- __ --------------------------------~ (Hin) .5 C ;::: .00012 .0002 .0003 .0004 s .4 6D/D Fi .3 .2~------~~------~------~U-----~~~----~ 1 - Suction Only 2 - Suction and !nje~tion 3 - Net (Suction, Injection and Momentum) I , .96 . !

.92

j

• 88 L- ____ .... --'- ___ .u... ___ --'-I-- ___ ~ ___ --'

o 5 10 15 20 25

'1 d FIGURE 27. REDUCED DRAG WITH COMBINED SUCTION AND INJECTION Ii

i

~ "

OF

o ~o

o

= 1 - .213

.-' =1-- -D-

o OF

o . o I with results as shown in Figure (27).

It is apparent that the greatest net drag reduction is obtained with the minimum suction flow. The injection slot height corresponding to this condition is extremely small, approximately one-tenth of an inch. It is Possible that a practical installation would require a larger slot height, obtainable by restricting the lateral extent of the slot. In this case, t~e contribution to drag reduction would be less than for the fully extend- ed slot. However, the slot injection contributes a minor part of the net drag reduction so that a larger slot height would not seriously affect the net. reduct i on.

Figure (27) shows that the minimum reduced drag ratio corresponding to the minimum suction flow is around .91 (9% drag reduction). The interpreta- tion of this ratio in terms of mission performance (range increase with the same fuel load or fuel load decrease with the same range) is presented in a later section.

C. Fuselage Suction - The scheme of combined suction and injection in- dicated that the contribution of injection to the net drag reduction is very sma 11. Th,e rea I advantage of the i nj ect ion is that it takes p] ace ina low pressure region on the top half of the fuselage, thus providing a means of discharging the suction flow without theneed of pumping or turbo-machines.

The disadvantage of the scheme is that it precludes achieving the larger drag reduction which would result if the upper part of the fuselage were also treated with suction. The use of suction over both halves of the fuselage would nearly double the reduction in skin friction and would more than off- set the drag due to the pumping required.

The use of turbo-machines to perform the pumping is neatly adaptable to the scheme of suction over the entire fuselage perimeter, permitting a system which eliminates the need for complicated ducting. As illustrated in Figure

(~8) the suction surface forms a shell around the pressurized fuselage sur- " " .

face with the annular space between the two surfaces forming a passageway which leads the suction flow to the compressor located at the aft end of the terminal fuselage taper. The turbine is located on the outside of the suc- tion surface where it handles the free stream boundary air produced by the suction process. The turbine and compressor comprise a single wheel with turbine blades on the outside and compressor blades on the inside. The sys- tem thus consists of an extremely simple and convenient arrangement of sur-' face, ducting and turbo-machinery.

To determine the net drag reduction of this scheme, the drag due to the turbo-machinery is accounted for by assuming intake and discharge pres- sures equal to free stream pressure. Then the drag of the compressor (sue- t ion flow) is given by

compressor drag = W (V

c co and for the turbine The value of V is the average velocity (based on momentum) of the boundary layer flow ingested by the turbine. To evaluate this parameter the asymptotic velocity profile for suction is assumed to prevail at this station. Accord- ing to Reference (6) (page 231) this is given by V/V = 1 - exp (-1;) ex> where ~ == C V I '> S Pex> ex> Y 11 Here y denotes distance measured normal to the wall. The suction flow coef- ficientis taken at the optimum value C = .00012 for this calculation.

s From the assumed velocity profile the average velocity is given by .'

Fuselage Turbine Suction Surface M ~-t----- ; FIGURE'2B. SCHEHATIC OF FUSELAGE SUCTION SYSTEH '~ITH TURBO-I~ACHINES " I .

250 __ ------------------------------------------~ . ; v, m/s , ..

.5 1.0 1.5 2.0 \UW s FIGURE 29., AVERAGE VELOCITY IN SUCTION BOUNDARY LAYER

1.4~--------------------------1 Pressure Ratio 1.1 1.0 .88 DID o .84 .6

.2 .4

EFFECT OF COI1PRESSOR DI SCHARr.E MACH NUt1~ER ON PRESSURE FIGURE 30.

RATIOS AND NET DRAG \~ITH FUSELAGE SUCTION

-2F; e )

V/V =

The flow in the boundary layer in terms of the suction flow is g'iven by By means of these equations, the average velocity V may be found as a func- tion of W/W. The results are shown in Figure (29).

s In applying these data to the turbo-machine, it is considered that the suction flow W is the compressor flow Wand the boundary layer flow W is s c the turbine flow W , \~hile the compressor flow is fixed by the suction re- t qui rements" the turbine flow may be chosen at wi 11, wi th the choice depend- ing on the effect on overall performance.

The power generated by the turbine in reducing the velocity from V, to V is absorbed by the compressor and utilized to reduce its drag by increas-

z

ing the discharge velocity V . In calculating the exchange and utilization of! power, turbine and compressor efficiencies are taken as .9 (justified by the low pressure ratio of the machines) and line loss recovery ,factors as .55 (justified by the small flows involved so that ducting losses can be made very small without compromising weight or space), It is also assumed tHat all the free stream velocity head is lost in the suction process so that the total Pl-cssure at the compressor face is given by kl x Poo where kl is the line loss recovery facto'r.

The compressor flow is fixed by the suction flow requirements, but the turbine flow is an independent design parameter which may be chosen for best overall performance. The compressor discharge velocity V3 (or the correspond- ing Mach number M ) is also an independent design parameter.

The effect of M3 is illustrated in Figure (30) which shows a typical

vari~tlon (calculated with Wc = W ) of the net drag {reduced skin friction

t

drag plus the momentum drags of the turbo-machine flows). It appears that the optimum M3 is around .4. HO\",ever, the effect on net drag is quite small and a value of M3 = .2 ,is preferable because it entai Is smaller pressure ratios of the compressor and turbine.

The effect of turbine flow is calculated with M3 = .2 and with V, de-

termined as a 'function of \"t from the bOIl!"idary layer data in Figure (29) with W/W = Wt/W. The results (Figure 31) indicate that for practical s c purposes the net drag is independent of turbine flow. Therefore, the flow r.a.te may be chosen on the bas i s of conven i ence of des i gn. The lowe r the flow rate, the higher is the required pressure ratio, two effects which are generally to be considered as opposing in achieving an optimum design. How- ever, in the present application, because flow rates and pressure ratios are very mild, neither quantity is of overriding importance. Therefore, it is considered that using a turbine flow equal to the compressor flow, leading to a turbine pressure ratio which is slightly higher than the compressor pressure ratio, is a good solution.

Included in Figure (31) is a line showing the drag reduction due to the suction only, indicating that the drag due to the turbo-machine is relatively small. Also ShoWh on the figure is the result for the previous scheme of suction on only the lower half of the fuselage. The comparison indicates the greatly superior drag reduction with full fuselage suction and turbo-machine.

Reduced drag as a function of turbo-machine efficiencies and line loss re- covery factor is illustrated in Figure (32). These results indicate that the effect of low efficiency is not significant and the effect of line loss is moderate.

Of course, a fair comparison must take into account the difference in weight of the two schemes, the difference being favorable to the half-suction scheme without turbo-machine. Such a comparison involves the mission per- formance treated in a later section.

I t II i f: ..

. 96 r-- No Turbine/Compressor Suction on Lower Surface ____ -.£;..-._L.-._I n_J_· e_c_t_i_on _on Upper Surface .92 ~ / , .

"-" .

i t .88 . .

~ Suction and Turbine/Compressor t : D/D 3·

-

I

'\

.. 84 I-- upper surf~ces) Suction Only (lower and = 12.4 kg/s)

L ,,:suction flow \~c

-

,

I I I I

.80 20 25 10 15 W , kg/s t NET DRAG WITH FUSELAGE SUCTION FIGURE 31.

_ .88~ _______________________________ --, DID o .84 .80 .7 .8 1.0 .9 k ;88 DID .84

-

I I

.80 '1

. : .8 1.0

.9 .

And n nc t FIGURE'32.

EFFECT OF TURBO-MACHINE EFFICIENCIES AND LINE LOSS RECOVERY , FACTOR ON NET DRAG WITH FUSELAGE SUCTION " 1 •

D. Wing Suction - To estimate potential drag reduction due to wing suction the two-dimensional resuits developed in Section IV-B were applied, on the average, to the total wing surface of the baseline configuration.

The essential features of this scheme are indicated in Figure (33).

Since the suction air processed by the compressor was collected at variable presure, a certain ambiguity arises in defining the total pres- sure P . Accordingly, an appropriate average value is needed to treat compressor performance. One approach is to weigh the pressure with re· spect to mass flow. If X represents the fraction of the flow at total pressure P, the average is given by P = f PdX or if the flow is considered to consist of discrete fractions or individ- ual flow filaments

'p = EX. P

I i In order to achieve this average in practice, it is necessary to preserve the individual flow filaments up to the compressor blading, a procedure which involves transcendent ducting problems. A much more feasible ap- proach is to consider the flows mixed before proceeding to the compressor, the ducting problem being reduced to providing a chamber where the in- dividual flow filaments may be mixed efficiently. In the case where this mixing is allowed to occur at constant area, mass and momentum conserva- t i oni mp ly that W N = EW.N.

I I where the W. represent the flow rates of the individual filaments and I 1 2 (1 + yM.)

N. = N.(M.) - (M.)

I I I I I

N = NUi) - (~)

M

~/ing Suction

MOO-->- __ -~::::=~E===::::7

Compressor Flow W c Compressor Total Pressure P 4 M2 I HI; Turbine Turbine Flow W t SCHEMATIC OF WING SUCTION ARRANGEMENT FIGURE 33.

In the latter expressions the Mi represent the Mach numbers of the individ- ual filaments at the start of the mixing process and M is the final Mach

number of the total mixed flow. W, of course, is the total mass flow and

is related to the W. by W = EW .. In deriving these relations it has been

I I assumed that all the filaments are parallel at the start of the mixing process and that each have the same total temperature. .

If it is now further assumed that all of the individual filaments are expanded to sonic velocity at the entrance to the mixing chamber then ....

N. = N" ::N(1) for all i

Accordingly, the relation for N yields

* - ';'\

N = (N /W) E W. = N

That is, the Mach number of the mixed flow is also sonic. It follows, there- fore, that W. P. A.

1 1

x. :: _I =

I W

PA

where x. is the fraction of flow at stagnation pressure P., P is the stagna-

1 I tion pressure of the mixed flow, and A. and A the respective flow areas.

Since we have assumed constant area mixing A = EA .• Thus

I or

P =

Applying this concept to the pressure distribution on the wing (Figure 2) the effective total pressure is determined as approximately

p /P = .75

co It is worth noting that this average pressure is around 90% of the basic av~r age determined by weighing with respect to flow.

in a manner is determined flows turbo-machine of the drag The momentum a pressure provides The compressor previously.

described to that similar ini- from its flow of the suction pressure the to increase sufficient ratio the discharge for due allowance Pm' with value to its discharge value P tial is fixed flow The compressor factor.

recovery 1 ine loss and the Mach number de- an independent flow is the turbine but requirements flow by the suction it is making calculations, will. In chosen at may be which sign parameter Mach exit the compressor H2 and Mach number exit ,the turbine to treat best for best per- may be chosen which design parameters M3 as independent number design parameter is also a number Ml Mach entrance The turbine formance.

to ingest be arranged flow can the turbine inlet of since the extent to some or wing.

fuselage along the layer flow boundary the in illustrated M3 is Mach number exit the compressor effect of The with = .82 and

M = Moo

drag with of net shows curves (34) which Figure t gives very since it for design is chosen M3 = .2 value of M • The various flow.

turbine smallest and the net drag the lowest nearly in Figure Mi is illustrated number exit Mach the turbine effect of The The figure results.

the best .4 gives of .3 or a value shows that (35) which M , indicating Mach number inlet of the turbine effect the also illustrates 1 of with the use occur of performance would deterioration that a serious low net drag and (low performance overall For best layer flow.

boundary and layer of the boundary be free should turbine inlet the turbine flow) flow.

free stream handle only should were de- and (35) Figures (34) in the results noted that should be It by defined the compressor at' totaLpressure average wi th the te!rmined is interesting value. It average realistic as a was chosen

= .75 which

~/p the by illustrated performance, on of this pressure effect the tq consider It is M2 = .4.

Moo = .82 and Ml = with (36) calculated in Figure results drag the net on both large effect has a pressure the average that apparent flow.

and the turbine presented are loss factors and line machine efficiencies effect of The a in points, result circled by the values, shown design (37). The in Figure

1.00~----------------------------------------~~----~ .6 .92 .4 DID "" o

.88

Skin Friction Only .80L-------~---------L--------~--------~------~ 30 .

40 60 80

50 70

I

FIGURE 34. EFFECT OF EXIT MACH NUMBERS ON NET DRAG WITH WING SUCTION.

1.00----------------------------------------------------~

•

.2 .96 .7=M

~

.4 .82

~

----G : .5 M =·4 .92 0/0 .88 Skin Friction Only .84 o o W , kg/s t EFFECT OF TURBINE ENTRANCE AND EXIT MACH NUMBERS ON NET DRAG FIGURE 35.

WITH WING SUCTION.

- .

, i.

.96 t

" ,..'

.7

.8

PIP =.9 .92 00 1.0

c_

-

~

.88

Skin Friction Only .84

1----------

.8o~--------~-------------------h------------------~ 10 20 30 l 40 50 60 W , kg Is t FI GURE 36. EFFECT OF AVERAGE SUCTI ON PRESSURE ON NET DRAG WITH WI NG SUCTI ON " 'j ,

1.0 Turbine Line Loss DID o

I

Compressor .92 Line Loss .88.

.8 1.0 7 .9 .96 ~----------.---- DID o .92 .88~------~~-----f--~------~ 1.0 .7 .8 .9 FIGURE 37. EFFECT OF TURBO-MACHINE EFFICIENCIES AND LINE LOSS RECOVERY FACTORS ON NET DRAG \-11TH \.JING SUCTION "

reduced net drag DIDo = .928. This is less than obtained with suction on the

fuselage for which DID = .844. Nevertheless, the reduction is significant

o and especially when used together with fuselage suction can produce much im- proved mission performance as will be demonstrated in the next section.

, . " The physical layout of the wing-suction scheme is conceived as two sepa- rate symmetrical arrangements of ducting and turbo-machine, one for each of the port and starboard wings. The ducting of the suction flow proceeds from the wing tip to thq wing root where the turbo-machine is located. For the baseline configuration the wing thickness at the root is approximately 2.1 m.

This is large enough to accommodate the turbo-machine, the diameter of which is estimated to be around 1.2 m. The inlet for the turbine flow may be lo- , , cated on the bottom of the wing or on the side of the fuselage. The size of the inlet is very small, the area being around .2 m for each side. The flow exits may be located on the fuselage near the trailing edge of the wing root or at the trailing edge of the wing itself. This latter arrangement could produce some improvement in airplane performance by delaying separa- tion on the wing.

VI. MISSION PERFORMANCE In order to evaluate the drag reduction schemes properly it is neces- sary to consider the effect on the mission performance of the airplane. For a realistic evaluation the added weight introduced by the scheme must be in- cluded in the analysis.

To keep the analysis simple, the mission is considered to consist of three parts.

(1) Initial operation prior to cruise (2) Cruise' (3) Final operation after cruise It is assumed that range is accomplished only in the cruise part of the mis- sion and that all the fuel has been consumed at the'end of the final opera- tion.

Let us consider first the mission for the baseline configuration i.e., in the absence of any drag reductiqn. Each part of the mission is character- ized by a certain fuel consumption defined by the three parameters.

= F1/Wo Y1

=

'i ." F2/Wo l.

.- Y

F /W

Q where F , F2 and F3 are the fuel weights con~umed during operations 1, 2 and and W is the gross weight of the airplane (weight at the start of operation 1).

o The total fuel consumed is given by W F =Y 0 0 where = Y + Y + Y Y o 1 2 and airplane weight after the mission is the over is

tv = W - F

e 0 The range accomplished during the mission is given by

R = constant (LID) log

(w- F - F f

o 1 2 where (LID) is the maximum lift to drag ratio of the airplane.

The constant is a function of the cruise speed and the engine perfor- mance, but its value is not pertinent for the present purpose since we will be dealing with relative mission performance.

Consider now the airplane with ~ ~rag reductfon scheme which decreases dr~g but increases weight. The decrease in drag increases the maximum LID.

With the assumption that the drag polar of the original airplane is parabolic and does not change in shape, the new maximum LID, denoted with a prime, may be expressed, in terms of the reduced drag DID determined in the previous . 0 sections of this report.

, (LID) = 2(0/0 ) - 1

1I7DT

o The variation of this ratio with DIDo is shown in Figure (38). If the drag reduction scheme did not introduce an increase in weight, this ratio would represent the relative increased range which would be accomplished by the

*

airplane with the same fuel load.

*It is important to note that the effect illustrated in Figure (38) assumes that changes in the drag polar are due solely to changes in zero-lift drag.

This is essentially true for the fuselage drag reduction schemes. However, for schemes involving wing-suction an additional influence must be accounted f~r, viz., the effect ot suction on lift characteristics. For the present e~ample it is estimated that an additional 2 percent increase in maximum LID i~ piovided by the wing-suction scheme. The basis for this estimate is out- liined in Appendix B.

1." r--------------------------------: 1.3 (LID)' (LID) 1.2 1.1 J.

1.0 .76 .80 .84 .88 .92 .96 1.0 DID , j' FIGURE 38.

INCREASED MAXIt1Ut~ LID \~ITH NET REDUCED DRAG I •

The wei9ht increase of the airplane is responsible for increased fuel consumption required to accomplish the various parts of the mission. The fuel consumed in parts 1 and 3 is assumed to increase directly with the weight of the airplane at the start or end of these parts, denoting the case of the air- plane with the drag reduction by prime quantities.

I I I W W + F 1 e

= W =

W + F o e I W e W- e The drag reduction scheme introduc.es om increase in weight flW so that I

W = W + flW

e e are considered.

compari son two relative missions completeness of the Now for I be the same or F = F .

fuel load is considered to first mission the For the given by there is an increase in range In this case, I I ( 1 log + X ) (LID) R = ( 1 R (LID) + X ) log where Y2 X =

2 1 - Y Y

1 2 (Y (1 - Y ) Y (1 - Y ) B + Y 3) I 1 0 0 X

=

.: Y . + B) (1 ( 1 - y Y2) ' 0 ,1 I In the latter expression for X , the quantity B represents the increased weight introduced by the drag reduction scheme, defined by

B = /5.WIW

o I

In the second mission the range is considered to be the same or R = R •

In this case, 'there' is a reduction in the fuel load given by

- Y + B I o

F IF =

Y (1 1 - Y Y1) o o where

a = (L/D)/(L/D)

In applying these equations, the weight increase is expressed by the parameter w which defines the weight increase per square foot of surface,

6W = w x iurface area

In the case of complete suction on the fuselage, the surface ,area is taken as the complete suction surface 1T x 6.1 x 61 = 1170 m. In this case the value of w represehts the weight of the suction surface which is conceived as an additional surface applied over the original fuselage, the gap between the two surfaces forming the duct which leads the suction flow to the tUl'"bo- machine. The value of w does not have to be increased for extraneous ducting, but it must include some fraction for the structure which supports the suc- tion surface. The value of w may also be adjusted to account for the weight of the turbo-machines. However, the turbo-machine is so small that its weight is unimportant compared to the weight of the suction surface.

In the case of combined fuselage suction and inject~on, the surface is taken as the suction surface on the bottom part of the fuselage or 1/2 x 1170

= 585 m • In this case the value of w is larger than the weight of suction sur-

face, since it must include the weight required to duct and inject the ~uction flow on the top ha Hof the fuselage.

Calculations were made using an original gross weight W = 340,000 kg

o and representative values for the fuel fractions of the original mission as fo 110,'15:

Y = .05

V = .30

Vj= .15

The values of DID were taken as .844 for the case of complete suction with o turbo-machine and .916 for the case of half-suction and half-injection with- , '- out turbo-machine.

The results are presented as curves of increased range (Figure 39) and decreased fuel load (Figure 40) as a function of the weight parameter. It is considered that the suction surface weight is around 2.5 kg/m (aluminum skin .076 cm thi~k with some allowance for structural support). Therefor~, for the case of tomplete suction, the range increase is around 18% or the fw:d reduc- tion is around 11%. For the case of combined suction and injection the value of w is increased 20% to account for the weight of ducting required for injec- tion. In this case the range increase is approximately 8% or the fuel reduc- tion is around 6%.

It is apparent that complete suction offers superior mission performar,t.~.

This is true even when the added weight of the turbo-machine is taken into ac- count. It has been estimated that the size of the wheel is less than 1.2 m in diameter. Since it is a single stage machine, the weight is probably around

150 kg. The added surface weight based on w = 2.5 kg/m is 2830 kg. There-

fore, the weight of the turbo-machines increases w from 2.5 to 2.65. This in- crease does not reduce mission performance significantly.

The effect of turbo-machine effici~ncies and line loss recovery factor on mission performance (determined with w = 2.5) are shown in Figures (41) and (42) for the case of full fuselage suction. It is evident that the effects are extremely mild, a direct result of the small flow involved in the suction pro- cess.

Mission performance for an aircraft utilizing the wing drag reduction scheme whether alone or in combin.ation with the two fuselage drag reduction schemes is shown in Figures (43) and (,44).

For the case of wing suction, mission performance is determined for the

surface area of 900 m and a value of 0/0 = .928~ {Note that the LID factor

o in Figure 38 is increased by 2 percent to account for the improvement of lift

1.25 1.20 Suct ion on Top amI Bottom with Turbine/Compressor 1. 15 R!/R Suction on Bottom Injection on Top 1.10 1.05 1.0

o 6 10

w, kg/m FIGUHf.: 39. I NCREASED RANGE ~/I TH FUSELAGE DRAG REDUCTI ON AS FUUCT I ON OF SURFACE \~E I GHT PARAMETER

1.0 Suction on Bottom Injection on Top F'/F .92 Suction on Top and Bottom .88 ,with Turbine/Compressor .84·oL--------~2--------~------~6--------~8--~--~10 w, kg/m FIGURE 40.

DECREASED FUEL LOAD \",ITH FUSELAGE DRAG REDUCTION AS FUNCTION OF SURFACE WEIGHT PARAMETER ..

1.20 r------------~---, R'/R 1. 16 1.12 .. , 1.20

(

R'/R 1. 16 I--

I

I

.

1. 12 . 8 .9 1.0

.7

, And n tlc t FIGURE 41. EFFECT OF TURBO-MACHINE EFFICIENCIES AND LINE LOSS RECOVERY FACTOR ON INCREASED RANGE WITH FUSELAGE SUCTION "

.92 FlfF .88

. 84 L--_--..L..---~-,J.I-----I

1.0 .7 .8 .9 .92 ..-------~------------.

FlfF .88 ~

I I

. 84 ~,--_-_....J-.,-,----....----- .......

1.0 . 7 .8 .9 FIGURE 42. EFFECT OF TURBO-MACHINE EFFICIENCIES .AltW LINE LOSS RECOVERY FACTOR ON REDUCED fUEL LOAD WITH FUSELAGE SUCTION

1.lio ~-----------------------t 1 - Wing Suction 2 - Fuselage Half Suction and Injection 3 Fuselage Suction 4 - Cqmbined 1 & 2 5 - Combined 1 & 3 1.35 1 .30 .

1.25 1.20.

R'IR 1.0 8 10 • 2 6 o I w, kg/m INCREASED RANGE WITH DiRAGREDUCTION SCHEMES AS FUNCTION FIGURE 43.

OF SURFACE WEIGHT PAlRAMiETER -, .

1 - Wing Suction t - Fuselage Half SuctIon and Injettion 3 - Fuselage Suction 4 Combined 1 & 2 5 - Combined 1 & 3 1.0 .-------------------------------------------~ FlfF .7~------~--------~-------L------~~----~ 4 6 o 2 w, kgfm FIGURE 41.. DECREASED FUEL LOAD WITH DRAG REDUCTION SCHEMES AS FUNCTION OF SURFACE WEIGHT PARAMETER ,.

characteristics with suction.) The appropriate value of the surface weight parameter is taken to be 40% higher then the basic weight 2.5 kg/m to ac- count for the ducting and turbo-machinery or w = 3.5 kg/m • As can be seen, the wing drag reduction scheme produces only moderate improvement, 8% in- crease in range or 5% decrease in fuel load. However, when combined with either of the fuselage drag reduction schemes the effect is magnified.

For the combined systems the value of DID for determining the LID o factor is given by

DID = (DID) + (DID) -

00 0 i where i = 2 or 3.

The significance of the subscripts is defined at the top of Fi gure (1+3).

The 2 percent factor due to lift augmentation is applied to the combined LID which is an approximation considered sufficiently accu- rate for the present purpose.

The approximate surface areas for the combined systems to which the re- spective weight parameters are applied are given by S = 5 + 5.

I The corresponding weight parameters are given by w + w.

5.

1 I I W

=

There Is obtained Using the results shown in Figures (43) and (44) together with these vdlues of w the performance of the various drag reduction schemes can be established.

These are summarized in Table I I below.

TABLE II SUMMARY OF MISSION PERFORMANCE FOR ..

VARIOUS DRAG ~EDUCTION SCHEMES .

.'

% Range % Fuel Load \'.

Scheme w, kg/m Increase ,Decrease r 1 8 3·5 "' 2 3.0 8 6 ",, 2.5 18 11 ,; 4 3.3 18 11 3.0 32 17 It is interesting to note that the combined performance is more than the sum of the individual performances.

The effect of turbo-machine efficiencies and line 10s5 recovery factor on mission performance with the combined systems is shown in Figures (45) and (46). The efficiencies and recovery factor refer to the wjng suction system slnce this system is much more sensitive to these quantities. Furthermore, t~e recovery factor refers to the suction or compressor flow circuit since t~is is the circuit where ducting can become a problem. The results indicate that even with poor turbo-machine efficiencies and low recovery factor or high duct loss, the combined fuselage and wing drag reduction schemes produce large improvements in mission performance.

c

1.36----------------------------

1. 32 . '.

1.28 1.24 ~ ________ L_--------~------~ 1.0 .9 .

. 7 .8 1.32 I R /R 1.28 1.0 1.24 .J .9 .3 ; nAnd n t n FIGURE 45. EFFECT OF TURBO-MACHINE EFFICIENCIES AND LINE LOSS RECOVERY FACTOR ON I NCREASED RANGE ,./1 TH COI1131 NED FUSELAGE AND WING DRAG REDUCTION SCHEME I ,

',;; .88 i" "'L I F IF .84 .80~------~--------~-------J 1.0 .8 .9 .7 .88 I F IF " .80.

1.0 .9 .8 FIGURE 46. EFFECT OF TURBO-MACHINE EFFICIENCIES AND LINE LOSS RECOVERY FACTOR ON DECREASED FUEL LOAD WITH COM- BINED FUSELAGE AND \~ING DRAG REDUCTION SCHEt~E

REMARKS VII. CONCLUDING it is section in the previous presented results of the On the basis in improvement corresponding and drag reduction significant that concluded by judicious achieved can be aircraft transport of subsonic the performance com- include These schemes.

layer control boundary of certain application the surfaces of various applied to and slot injection suction of binations ai rcraft.

are subject study in' this obtained the results that It is emphasized the render which assumptions, and/or restrictions important number of to a and quantitatively.

qualitatively both provisional conclusion cited above here.

be delineated will restrictions These to relates studies in these implicit assumption fundamental The most with distrib- layer state boundary laminar the of preserving possibility the if since, crucial particularly is This assumption suction.

surface uted would actually drag the viscous conditions, under these occur did transition feasibility the values. Although turbulent the undisturbed above be increased and tunnel in both wind established have been appears to technique of the or commercial on either to date been made have no applications tests flight results have our performance Accordingly, 1).

(Reference aircraft military time.

at the present optimistic overly considered to be to be do prove assumptions aforementioned if the other hand, On the con- are probably obtained have been.

which estimates performance the valid, drag reduction the wing an example As of re.asons.

for a variety servative sen- was quite reduction that net indicated Section V-D in results outlined The per- Figure 36).

(cf: compressor at the pressure to the average sitive of single value with a VI were made Section in presented formance results would average of this Higher values = 0.75.

as PIP taken this parameter .

• by be achieved These could in performance.

increases substantial lead to ve- cost of increased at the possibly ducting more compelx of installation wing geometry.

of is a function parameter this Furthermore, weight.

hicle im- lead to and could be useful would this parameter of optimization Thus,

'proved performance.

Additional examples of possible improvement in performance would in- clude application of suction on empennage surfaces. The results given in Appendix A are indicative of the large reduction in drag that can be achieved by application of this technique on airfoil sections at zero angle of attack.

We also note that the contribution of those schemes to lift-augmentation has hardly been examined. Specifically, the angle of attack for which our wing results were made was substantially below representative values for flight at (LID) . It is expected that much greater improvement in (LID) would max max result at higher angles of attack. Also,the use of slot injection on the wings to energize ~he boundary layer and prevent separation has also not been examined.

In summary, the results of this study indicate a real potential in terms of the development of low-drag subsonic transport. However, the extent of this potential has not been completely established and further in-depth studies directed toward optimizing this potential are recommended.

"

..

REFERENCES 1. Head, M. R., Johnson, D. and Coxon, M., "Flight Experiments on Boundary Layer Control for Low Drag," ARC R & M 3025, March, 1955.

2. Whites, R. C., Sudderth, R. W. and Wheldon, \,~. G., "Laminar Flow Con- trol on the X-21," Astronautics and AeronauUcs, July, 1966 • Pfenninger, W., "Recent Development in Boundary Layer Research," AGARDO- 3.

graph 97, Vol. 4, 1965.

4. Groth, E. E. et aI, "Experimental Aerodynamic Investigations at Super-

sonic Speeds," Section I I, Part 2 of Summary of Laminar Boundary Layer Control Research, Technical Documentary Report ASD-TDR-63-554, March, 1964.

5. Jane.s All The Worlds Ai rcraft 1968-1969, McGraw-Hi 11 Book Co., New York.

6. Schlichting, H., "Boundary Layer Theory," Pergamon Press, 1955.

7. Beckwith, I. E. and Bushnell, D. M., "Calculation by a Finite-Difference

Method of Supersonic Turbulent Boundary Layers with Tangential Slot In- jection," NASA TN 0-6221, April, 1971.

8. Laitone, E. V., "Subsonic Flow About a Body of Revolution," Quart. App.

Math., i, 2, 227 (1947).

9. Bavitz, P., "An Analysis Method for Two-Dimensional Transonic Viscous Flow,1I NASA TN 0-7718, 1974.

10. Torda, T. P., "Boundary Layer Control by Continuous Surface Suction or Injection," J. Math. Phys., Vol. 31, p. 206, 1952.

11. Thwaites, B., "The Development of Laminar Boundary Layers under Condi- tions of Continuous Suction. Part I I: Approximate Methods of Solu- tion," Rep. Aero. Res. Coun., London, No. 12699.

12. Economos, C. and Fort, R., "Two-Dimensional and Axisymmetric Laminar and Turbulent Boundary Layer with Transition Criterion and Entropy Swal1owing," General Applied Science Laboratories, Technical Report No. 772, March, 1972 ..

13. Howard, F. G., J. N. Hefner and Srokowski, A. J., "Multiple Slot Ski'n Friction Reduction," to be published in the AIAA Journal of Aircraft.

14. Price, J. M. and Harris, J. E., "Computer Program for Solving Compres- sible Nonsimilar-Boundary-Layer Equations for Laminar, Transitional or Turbulent flows of a Perfect Gas ," NASA TM X-2458, Apri 1, 1972.

REFERENCES (Continued) 15. Cary, A. M. Jr. and Hefner, J. N., "Film Cooling Effectiveness and Skin Friction in Hypersonic Turbulent Flow," AIAA J. Vol. 10, No.9, Sep tembe r, 1972.

Kacker, S. C. and \~hitelaw, J. H., "Prediction of \~all-Jet and Wall- 16.

Wake Flows," Journal of Mechanical Engineering Science, Vol. 12, No.

6, pp. 404-420, 1970.

Saland, H. J., "Velocity Profi les for Tangential Slot Injection in 17.

Turbulent Incompressible and Compressible Flows," Ph. D. Thesis, New York University, 1970.

Grey, J., Ai rcraft Fuel Conservation: An AIAA View, Proceedings of 18.

a Workshop Conference, Reston, Virginia,' June, 1974.

AGARD, Transonic Aerodynamics, AGARD Conference Proceedings No. 35, 19.

Septembe r, 1968.

APPENDIX A LAMINAR BOUNDARY LAYER WITH SIMULTANEOUS MASS TRANSFER AND PRESSURE GRADIENT The starting point for this analysis is the Von Karman momentum inte- gral equation for two-dimensional incompressible laminar boundary layer flow which takes the form (cf: Reference 6, p. 236) du T U ~=~+v u (A-l ) e dx p w e where v represents the normal velocity at the wall (negative for suction) w and the remaining variables are defined in the conventional manner.

Equation (A-l) can be written in 'the alternate form I (A-2) U T' + T{H + 2) UU = C /2 + VU f where the transformed variables are defined by /u U u - eoo e V v /u - oo w e T u e/v , (A-3) - oo e ...

H o"/e - I } { d/dX - X u x/v - oo e , Following Tord~ (Reference 11) we assume a velocity profile of the form 'U 2 4 (A-4) Cn + Dn u = An + Bn + where 'U u/u u = e = ylo n

rr )'

r

Equation (A-4) satisfies the no-slip condition u(x,O) = O. The remaining coefficients are evaluated by imposing the following additional boundary conditions au .

0 @ y 0 -= = u u = ay e' du (A-S) (!J!)

~+ v (~) = u v e dx w ay w a 2 y w (!J!)

(!J!)

= v w a 2 ay3 y w w yields profi le (A-4) (A-S) to the Application of = (24 + 6N + MN)/K A = 3(4r~ 3N)/K B 3MN)/K (4M -

c --

(3N - 6 + 2MN - 6M - 3M2)/K D = where 18 + 6M + M2 K - ", VR M - I R2 U N - u o/v R - em also Substitution of these results in Equation (A-2) yields the following equation relating R, the Reynolds number based on boundary layer thickness, to the variation of mass transfer V and velocity U.

I (A-6)

V =

where

G = (1260K /B ) {N (B /1260K -1) + M + 6 /K} 4 5 l G = 26163 G = 66 /6 3 3 and 6 = (9180N + 7128N - 175392) + M(7290N - 10584N - 181728) + M2(2112N - 11388N - 86112) + M3(291N - 3276N - 21936) + M4(19N£ - 416N - 3768) - M (26N + 432) - 24M

6 = (11016N + 7128) + M(9126N - 6156) + M2(3114N - 8064)

+ M3(513N - 3048) + M4(38N - 546) - 39M5

6 = (1890N + 26568N + 19008) + M(~898N2 + 19944N + 12672)

+ M2(909N2 + 1368N - 19008) + M3(76N - 780N - 4032) - M4(78N + 144) 6 = 72(17N + 211N + 1778) + 6M(101N + 1007N + 10838) I ..

+ 2M2(38N + 32tN + 9108) + 3M (tlN + 936) + 216M 6 = 6N + 24 + MN For given distributions of V and U the variation of boundary layer thickness can be determined from Equation (A-6). Subsequently, all other boundary layer parameters (momentum thickness, skin friction, etc.) can be computed from ap- propriate algebrais auxiliary relations. Alternately, the condition R=O can be imposed leading to I (A-7) V =

Then for U specified the requisite distribution of suction needed to main- tain a constant boundary layer thickness can be established.

Two features of Equations (A-6) and (A-7) are important to note here.

First, the solution depends on the second derivative of the axial velocity distribution. Accordingly, in the numerical integration procedure which was utilized to obtain solutions a CUbic-spline fit of the input velocity dis- tribution was employed to assure smooth variation of this parameter.

The second feature to be noted is that the leading term on the right hand side of either (A-61 or (A-7) is singular at a stagnation point; i.e.: G has no real roots. Accordingly, this method cannot be utilized to initiate , '<$',I'J a calculation at a stagnation point. Thus, the approximate scheme due to Thwaites (Reference 11) was employed for this purpose and the two methods matched at a small distance away from the singularity. The method of Re- ference (11) takes the following form. Equation (A-2) can be written ,. r I (A-8)

Z = P/U

where T2

z

2 {c /2U - T2 U' (H + 2) + VT} P f Thwaites approximates the function P by P = 0.45 - 6T2 U' 1.28 VT + 0.76 V T2 Real roots of this function can be found. Accordingly, the indeterminate form P/U at a stagnation point can be evaluated permitting integration to it: be initiated there. Specifically, it can be shown that 2 II • 2 T U P - V • o o. 0

z

=

o : ~ *This procedure represents a generalization of the method employed in the : § !<.arman-Pohlhausen technique to evaluate stagnation conditions in the ab- sence of mass transfer (see p. 210 of Reference 6).

1.5 1.0 pIp <Xl .5 .004 ~----------------------------------~ 1000 C .003 .002 .001

o

t

1000 C 5 _=.....:;......---:, . ..:.l_v-------- ...., .. o..:,lJ.9

Separation

I I

.8 1.0 o .2 .4 .6 x/c fiGURE A-1. CHORDWISE VARiATION OF LOCAL SKIN FRICTION AND SEPARATION ON AN AIRFOIL I/ITH UNIFORM SUCTION J01

1.0 .8 Separat ion .6 Occurs .4 .2 Optimum o 0 .2 .4 .6 .8 1.0 FIGURE A-2. NET REDUCTION IN AVERAGE SKIN FRICTION DRAG AS A FUNCT I ON OF SUeT ION PARN1ETER

where -6 -1.28 + 1.52 V T o 0 and the subscript 0 denotes values at the stagnation point • A computer code was developed for numerical solution of Equations (A-6) and (A-7) by standard integration techniques. Some representative results obtained with this scheme are presented in Figure (A-l). Here the variation of skin friction coefficient over an airfoi I surface with the. indicated pres- sure distribution for various uniform rates of suction are presented. The selected pressure distribution is nominal but corresponds roughly to that

encountered on a symmetric airfoil at a free stream Mach number of M = .75

(Reference 19). As can be seen, for suction rate~ moderately greater than the optimum value separation is suppressed with substantial reduction in skin friction relative to the turbu.lent estimates which are also shown. These re- suIts are sumnarized in Figure (A-2) in terms of net reduction in average skin friction as a function of the suction flow coefficient.

APPENDIX B liFT AUGMENTATION DUE TO WING SUCTION According to Reference (9), the section lift coefficient corresponding to the inviscid pressure distribution shown in Figure (2) is 1.084. Further it is indicated that if viscous effects are taken into account the lift co- The pressure drag coefficient is efficient is reduced to a value .779 .

• 00266.

For the purpose of the present estimate it is assumed that the higher value of C can be attained when suction is applied in accordance with the l distribution shown in Figure (6). In the absence of suction the lower value prevai ls.

It is now assumed that the two-dimensional pressure drag varies as the square of the lift, similar to the variation of the nominal drag polar which has the form CD = Co + k C~. In this form, the factor k is considered to be 9dimensional the sum of the three induced drag factor and the two-dimensional pressure drag factor. Without improved lift, the k-factor due to pressure drag is given by where cOp is the pressure drag coefficient and ell is the smaller of the stated lift coefficients.

Assuming that the chan,ge in pressure drag is small, the.k-factor with i mp roved 1i f tis

k2 = Co tC

l p 2 The improved maximum liD is then given by k.

(LlO)2 + kl I

=

k.

(LID) 1 + k2 I

where k. is the three-dimensional induced drag factor.

To evalua.te the improvement, the value of k. is taken as .1 .045 =

k. = =

'If X Aspect Ratio 'If X 7 Substitution of the ~umerical data yields (L/D)2 .045 + .0044 IV 1.02 = .045 + .0023 ( LID) 1